LMFDB - Embedded newform 756.2.bi.c.559.39

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(307,756)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("756.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bi (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			559.39
Character	$\chi$	$=$	756.559
Dual form			756.2.bi.c.307.39

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41265 - 0.0664123i) q^{2} +(1.99118 - 0.187635i) q^{4} +(-2.66647 + 1.53948i) q^{5} +(1.15806 - 2.37885i) q^{7} +(2.80038 - 0.397302i) q^{8} +O(q^{10})$	\(q+(1.41265 - 0.0664123i) q^{2} +(1.99118 - 0.187635i) q^{4} +(-2.66647 + 1.53948i) q^{5} +(1.15806 - 2.37885i) q^{7} +(2.80038 - 0.397302i) q^{8} +(-3.66455 + 2.35184i) q^{10} +(3.64870 + 2.10658i) q^{11} +(2.97309 - 1.71651i) q^{13} +(1.47795 - 3.43739i) q^{14} +(3.92959 - 0.747231i) q^{16} +2.29127i q^{17} +1.70965 q^{19} +(-5.02055 + 3.56571i) q^{20} +(5.29425 + 2.73354i) q^{22} +(-4.68317 + 2.70383i) q^{23} +(2.24003 - 3.87984i) q^{25} +(4.08594 - 2.62229i) q^{26} +(1.85954 - 4.95400i) q^{28} +(4.76517 - 8.25352i) q^{29} +(3.22265 + 5.58179i) q^{31} +(5.50152 - 1.31655i) q^{32} +(0.152169 + 3.23677i) q^{34} +(0.574276 + 8.12592i) q^{35} -2.04135 q^{37} +(2.41514 - 0.113542i) q^{38} +(-6.85549 + 5.37054i) q^{40} +(4.43693 - 2.56166i) q^{41} +(2.89849 + 1.67344i) q^{43} +(7.66048 + 3.50995i) q^{44} +(-6.43612 + 4.13059i) q^{46} +(-2.20674 + 3.82219i) q^{47} +(-4.31781 - 5.50968i) q^{49} +(2.90671 - 5.62963i) q^{50} +(5.59787 - 3.97574i) q^{52} -10.5744 q^{53} -12.9722 q^{55} +(2.29788 - 7.12178i) q^{56} +(6.18340 - 11.9758i) q^{58} +(-4.44595 - 7.70061i) q^{59} +(-3.57388 - 2.06338i) q^{61} +(4.92318 + 7.67111i) q^{62} +(7.68430 - 2.22520i) q^{64} +(-5.28509 + 9.15404i) q^{65} +(-9.53591 + 5.50556i) q^{67} +(0.429923 + 4.56233i) q^{68} +(1.35091 + 11.4410i) q^{70} +2.48841i q^{71} +3.46980i q^{73} +(-2.88373 + 0.135571i) q^{74} +(3.40422 - 0.320791i) q^{76} +(9.23662 - 6.24015i) q^{77} +(-8.87914 - 5.12638i) q^{79} +(-9.32776 + 8.04200i) q^{80} +(6.09771 - 3.91340i) q^{82} +(0.0572673 - 0.0991899i) q^{83} +(-3.52738 - 6.10959i) q^{85} +(4.20570 + 2.17150i) q^{86} +(11.0547 + 4.44959i) q^{88} +3.61933i q^{89} +(-0.640313 - 9.06033i) q^{91} +(-8.81769 + 6.26253i) q^{92} +(-2.86352 + 5.54598i) q^{94} +(-4.55872 + 2.63198i) q^{95} +(-5.53677 - 3.19666i) q^{97} +(-6.46548 - 7.49651i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 6 q^{2} - 2 q^{4} + 24 q^{8}+O(q^{10}) $ 80 * q + 6 * q^2 - 2 * q^4 + 24 * q^8	$ 80 q + 6 q^{2} - 2 q^{4} + 24 q^{8} - 10 q^{14} - 18 q^{16} - 14 q^{22} + 32 q^{25} + 28 q^{28} - 8 q^{29} + 16 q^{32} - 16 q^{37} + 84 q^{44} + 24 q^{46} - 24 q^{49} + 12 q^{50} + 48 q^{53} - 32 q^{56} - 14 q^{58} - 8 q^{64} + 40 q^{65} - 22 q^{70} - 64 q^{74} + 12 q^{77} + 40 q^{85} + 52 q^{86} + 6 q^{88} - 30 q^{92} - 20 q^{98}+O(q^{100}) $ 80 * q + 6 * q^2 - 2 * q^4 + 24 * q^8 - 10 * q^14 - 18 * q^16 - 14 * q^22 + 32 * q^25 + 28 * q^28 - 8 * q^29 + 16 * q^32 - 16 * q^37 + 84 * q^44 + 24 * q^46 - 24 * q^49 + 12 * q^50 + 48 * q^53 - 32 * q^56 - 14 * q^58 - 8 * q^64 + 40 * q^65 - 22 * q^70 - 64 * q^74 + 12 * q^77 + 40 * q^85 + 52 * q^86 + 6 * q^88 - 30 * q^92 - 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.41265	−	0.0664123i	0.998897	−	0.0469606i
$2$	1.41265	−	0.0664123i	0.998897	−	0.0469606i
$3$		0			0
$3$		0			0
$4$	1.99118	−	0.187635i	0.995589	−	0.0938176i
$5$	−2.66647	+	1.53948i	−1.19248	+	0.688479i	−0.958868	−	0.283851i	$-0.908388\pi$
$5$	−2.66647	+	1.53948i	−1.19248	+	0.688479i	−0.233612	+	0.972330i	$0.575054\pi$
$6$		0			0
$7$	1.15806	−	2.37885i	0.437704	−	0.899119i
$7$	1.15806	−	2.37885i	0.437704	−	0.899119i
$8$	2.80038	−	0.397302i	0.990085	−	0.140468i
$9$		0			0
$10$	−3.66455	+	2.35184i	−1.15883	+	0.743719i
$11$	3.64870	+	2.10658i	1.10012	+	0.635157i	0.936254	−	0.351325i	$-0.114269\pi$
$11$	3.64870	+	2.10658i	1.10012	+	0.635157i	0.163870	+	0.986482i	$0.447602\pi$
$12$		0			0
$13$	2.97309	−	1.71651i	0.824586	−	0.476075i	−0.0274094	−	0.999624i	$-0.508726\pi$
$13$	2.97309	−	1.71651i	0.824586	−	0.476075i	0.851995	+	0.523549i	$0.175392\pi$
$14$	1.47795	−	3.43739i	0.394998	−	0.918682i
$15$		0			0
$16$	3.92959	−	0.747231i	0.982397	−	0.186808i
$17$			2.29127i			0.555715i	0.960622	+	0.277857i	$0.0896242\pi$
$17$			2.29127i			0.555715i	−0.960622	+	0.277857i	$0.910376\pi$
$18$		0			0
$19$	1.70965			0.392221			0.196110	−	0.980582i	$-0.437169\pi$
$19$	1.70965			0.392221			0.196110	+	0.980582i	$0.437169\pi$
$20$	−5.02055	+	3.56571i	−1.12263	+	0.797318i
$21$		0			0
$22$	5.29425	+	2.73354i	1.12874	+	0.582794i
$23$	−4.68317	+	2.70383i	−0.976507	+	0.563787i	−0.901214	−	0.433375i	$-0.857323\pi$
$23$	−4.68317	+	2.70383i	−0.976507	+	0.563787i	−0.0752935	+	0.997161i	$0.523989\pi$
$24$		0			0
$25$	2.24003	−	3.87984i	0.448005	−	0.775968i
$26$	4.08594	−	2.62229i	0.801319	−	0.514273i
$27$		0			0
$28$	1.85954	−	4.95400i	0.351421	−	0.936218i
$29$	4.76517	−	8.25352i	0.884870	−	1.53264i	0.0390079	−	0.999239i	$-0.487580\pi$
$29$	4.76517	−	8.25352i	0.884870	−	1.53264i	0.845862	−	0.533401i	$-0.179086\pi$
$30$		0			0
$31$	3.22265	+	5.58179i	0.578805	+	1.00252i	0.995617	+	0.0935263i	$0.0298139\pi$
$31$	3.22265	+	5.58179i	0.578805	+	1.00252i	−0.416812	+	0.908993i	$0.636853\pi$
$32$	5.50152	−	1.31655i	0.972540	−	0.232736i
$33$		0			0
$34$	0.152169	+	3.23677i	0.0260967	+	0.555102i
$35$	0.574276	+	8.12592i	0.0970704	+	1.37353i
$36$		0			0
$37$	−2.04135			−0.335597			−0.167798	−	0.985821i	$-0.553666\pi$
$37$	−2.04135			−0.335597			−0.167798	+	0.985821i	$0.553666\pi$
$38$	2.41514	−	0.113542i	0.391788	−	0.0184189i
$39$		0			0
$40$	−6.85549	+	5.37054i	−1.08395	+	0.849157i
$41$	4.43693	−	2.56166i	0.692931	−	0.400064i	−0.111778	−	0.993733i	$-0.535655\pi$
$41$	4.43693	−	2.56166i	0.692931	−	0.400064i	0.804709	+	0.593669i	$0.202321\pi$
$42$		0			0
$43$	2.89849	+	1.67344i	0.442015	+	0.255198i	0.704452	−	0.709752i	$-0.251193\pi$
$43$	2.89849	+	1.67344i	0.442015	+	0.255198i	−0.262437	+	0.964949i	$0.584526\pi$
$44$	7.66048	+	3.50995i	1.15486	+	0.529144i
$45$		0			0
$46$	−6.43612	+	4.13059i	−0.948954	+	0.609022i
$47$	−2.20674	+	3.82219i	−0.321886	+	0.557524i	−0.980877	−	0.194627i	$-0.937650\pi$
$47$	−2.20674	+	3.82219i	−0.321886	+	0.557524i	0.658991	+	0.752151i	$0.270984\pi$
$48$		0			0
$49$	−4.31781	−	5.50968i	−0.616830	−	0.787097i
$50$	2.90671	−	5.62963i	0.411071	−	0.796151i
$51$		0			0
$52$	5.59787	−	3.97574i	0.776285	−	0.551336i
$53$	−10.5744			−1.45250			−0.726250	−	0.687431i	$-0.758738\pi$
$53$	−10.5744			−1.45250			−0.726250	+	0.687431i	$0.758738\pi$
$54$		0			0
$55$	−12.9722			−1.74917
$56$	2.29788	−	7.12178i	0.307068	−	0.951688i
$57$		0			0
$58$	6.18340	−	11.9758i	0.811920	−	1.57250i
$59$	−4.44595	−	7.70061i	−0.578813	−	1.00253i	−0.995616	−	0.0935372i	$-0.970183\pi$
$59$	−4.44595	−	7.70061i	−0.578813	−	1.00253i	0.416802	−	0.908997i	$-0.363151\pi$
$60$		0			0
$61$	−3.57388	−	2.06338i	−0.457588	−	0.264189i	0.253441	−	0.967351i	$-0.418437\pi$
$61$	−3.57388	−	2.06338i	−0.457588	−	0.264189i	−0.711030	+	0.703162i	$0.751771\pi$
$62$	4.92318	+	7.67111i	0.625245	+	0.974232i
$63$		0			0
$64$	7.68430	−	2.22520i	0.960538	−	0.278150i
$65$	−5.28509	+	9.15404i	−0.655535	+	1.13542i
$66$		0			0
$67$	−9.53591	+	5.50556i	−1.16500	+	0.672611i	−0.952496	−	0.304550i	$-0.901494\pi$
$67$	−9.53591	+	5.50556i	−1.16500	+	0.672611i	−0.212500	+	0.977161i	$0.568161\pi$
$68$	0.429923	+	4.56233i	0.0521358	+	0.553264i
$69$		0			0
$70$	1.35091	+	11.4410i	0.161465	+	1.36746i
$71$			2.48841i			0.295320i	0.989038	+	0.147660i	$0.0471741\pi$
$71$			2.48841i			0.295320i	−0.989038	+	0.147660i	$0.952826\pi$
$72$		0			0
$73$			3.46980i			0.406110i	0.979167	+	0.203055i	$0.0650870\pi$
$73$			3.46980i			0.406110i	−0.979167	+	0.203055i	$0.934913\pi$
$74$	−2.88373	+	0.135571i	−0.335226	+	0.0157598i
$75$		0			0
$76$	3.40422	−	0.320791i	0.390491	−	0.0367972i
$77$	9.23662	−	6.24015i	1.05261	−	0.711131i
$78$		0			0
$79$	−8.87914	−	5.12638i	−0.998982	−	0.576762i	−0.0910349	−	0.995848i	$-0.529017\pi$
$79$	−8.87914	−	5.12638i	−0.998982	−	0.576762i	−0.907947	+	0.419085i	$0.862351\pi$
$80$	−9.32776	+	8.04200i	−1.04287	+	0.899123i
$81$		0			0
$82$	6.09771	−	3.91340i	0.673380	−	0.432163i
$83$	0.0572673	−	0.0991899i	0.00628591	−	0.0108875i	−0.862865	−	0.505434i	$-0.831332\pi$
$83$	0.0572673	−	0.0991899i	0.00628591	−	0.0108875i	0.869151	+	0.494546i	$0.164666\pi$
$84$		0			0
$85$	−3.52738	−	6.10959i	−0.382598	−	0.662678i
$86$	4.20570	+	2.17150i	0.453512	+	0.234159i
$87$		0			0
$88$	11.0547	+	4.44959i	1.17844	+	0.474328i
$89$			3.61933i			0.383648i	0.981429	+	0.191824i	$0.0614403\pi$
$89$			3.61933i			0.383648i	−0.981429	+	0.191824i	$0.938560\pi$
$90$		0			0
$91$	−0.640313	−	9.06033i	−0.0671230	−	0.949781i
$92$	−8.81769	+	6.26253i	−0.919307	+	0.652914i
$93$		0			0
$94$	−2.86352	+	5.54598i	−0.295350	+	0.572025i
$95$	−4.55872	+	2.63198i	−0.467715	+	0.270035i
$96$		0			0
$97$	−5.53677	−	3.19666i	−0.562174	−	0.324571i	0.191844	−	0.981426i	$-0.438553\pi$
$97$	−5.53677	−	3.19666i	−0.562174	−	0.324571i	−0.754018	+	0.656854i	$0.771887\pi$
$98$	−6.46548	−	7.49651i	−0.653112	−	0.757262i
$99$		0			0
$100$	3.73230	−	8.14576i	0.373230	−	0.814576i
$101$	−14.8206	−	8.55666i	−1.47470	−	0.851420i	−0.475109	−	0.879927i	$-0.657591\pi$
$101$	−14.8206	−	8.55666i	−1.47470	−	0.851420i	−0.999594	+	0.0285076i	$0.990925\pi$
$102$		0			0
$103$	−0.807160	−	1.39804i	−0.0795318	−	0.137753i	0.823516	−	0.567293i	$-0.192009\pi$
$103$	−0.807160	−	1.39804i	−0.0795318	−	0.137753i	−0.903048	+	0.429540i	$0.858676\pi$
$104$	7.64381	−	5.98811i	0.749537	−	0.587182i
$105$		0			0
$106$	−14.9379	+	0.702268i	−1.45090	+	0.0682103i
$107$		−	1.84363i		−	0.178231i	−0.996021	−	0.0891153i	$-0.971596\pi$
$107$		−	1.84363i		−	0.178231i	0.996021	−	0.0891153i	$-0.0284040\pi$
$108$		0			0
$109$	−2.66853			−0.255599			−0.127800	−	0.991800i	$-0.540791\pi$
$109$	−2.66853			−0.255599			−0.127800	+	0.991800i	$0.540791\pi$
$110$	−18.3252	+	0.861512i	−1.74724	+	0.0821420i
$111$		0			0
$112$	2.77314	−	10.2132i	0.262037	−	0.965058i
$113$	0.626681	+	1.08544i	0.0589532	+	0.102110i	0.893996	−	0.448075i	$-0.147890\pi$
$113$	0.626681	+	1.08544i	0.0589532	+	0.102110i	−0.835043	+	0.550185i	$0.814557\pi$
$114$		0			0
$115$	8.32500	−	14.4193i	0.776310	−	1.34461i
$116$	7.93966	−	17.3283i	0.737179	−	1.60890i
$117$		0			0
$118$	−6.79200	−	10.5830i	−0.625255	−	0.974247i
$119$	5.45058	+	2.65342i	0.499654	+	0.243239i
$120$		0			0
$121$	3.37533	+	5.84625i	0.306848	+	0.531477i
$122$	−5.18568	−	2.67749i	−0.469490	−	0.242409i
$123$		0			0
$124$	7.46421	+	10.5097i	0.670306	+	0.943795i
$125$		−	1.60090i		−	0.143189i
$126$		0			0
$127$			10.6611i			0.946022i	0.881056	+	0.473011i	$0.156833\pi$
$127$			10.6611i			0.946022i	−0.881056	+	0.473011i	$0.843167\pi$
$128$	10.7075	−	3.65377i	0.946416	−	0.322950i
$129$		0			0
$130$	−6.85806	+	13.2825i	−0.601491	+	1.16495i
$131$	4.50282	+	7.79911i	0.393413	+	0.681411i	0.992897	−	0.118975i	$-0.0379609\pi$
$131$	4.50282	+	7.79911i	0.393413	+	0.681411i	−0.599484	+	0.800387i	$0.704628\pi$
$132$		0			0
$133$	1.97987	−	4.06699i	0.171677	−	0.352653i
$134$	−13.1053	+	8.41075i	−1.13213	+	0.726578i
$135$		0			0
$136$	0.910327	+	6.41644i	0.0780599	+	0.550205i
$137$	−1.11722	+	1.93509i	−0.0954509	+	0.165326i	−0.909797	−	0.415054i	$-0.863763\pi$
$137$	−1.11722	+	1.93509i	−0.0954509	+	0.165326i	0.814346	+	0.580380i	$0.197096\pi$
$138$		0			0
$139$	5.09811	+	8.83019i	0.432416	+	0.748967i	0.997081	−	0.0763537i	$-0.0243278\pi$
$139$	5.09811	+	8.83019i	0.432416	+	0.748967i	−0.564665	+	0.825320i	$0.690994\pi$
$140$	2.66820	+	16.0724i	0.225504	+	1.35837i
$141$		0			0
$142$	0.165261	+	3.51526i	0.0138684	+	0.294994i
$143$	14.4639			1.20953
$144$		0			0
$145$			29.3436i			2.43686i
$146$	0.230438	+	4.90163i	0.0190712	+	0.405662i
$147$		0			0
$148$	−4.06470	+	0.383030i	−0.334116	+	0.0314849i
$149$	−6.16913	−	10.6853i	−0.505395	−	0.875370i	−0.999981	−	0.00624098i	$-0.998013\pi$
$149$	−6.16913	−	10.6853i	−0.505395	−	0.875370i	0.494585	−	0.869129i	$-0.335320\pi$
$150$		0			0
$151$	−9.36053	−	5.40430i	−0.761749	−	0.439796i	0.0681743	−	0.997673i	$-0.478283\pi$
$151$	−9.36053	−	5.40430i	−0.761749	−	0.439796i	−0.829923	+	0.557877i	$0.811616\pi$
$152$	4.78768	−	0.679248i	0.388332	−	0.0550943i
$153$		0			0
$154$	12.6337	−	9.42860i	1.01805	−	0.759778i
$155$	−17.1862	−	9.92243i	−1.38043	−	0.796989i
$156$		0			0
$157$	21.4858	−	12.4049i	1.71476	−	0.990015i	0.786896	−	0.617085i	$-0.211687\pi$
$157$	21.4858	−	12.4049i	1.71476	−	0.990015i	0.927860	−	0.372930i	$-0.121647\pi$
$158$	−12.8836	−	6.65211i	−1.02496	−	0.529213i
$159$		0			0
$160$	−12.6428	+	11.9800i	−0.999501	+	0.947105i
$161$	1.00861	+	14.2717i	0.0794898	+	1.12477i
$162$		0			0
$163$			10.9277i			0.855920i	0.903798	+	0.427960i	$0.140768\pi$
$163$			10.9277i			0.855920i	−0.903798	+	0.427960i	$0.859232\pi$
$164$	8.35405	−	5.93325i	0.652342	−	0.463309i
$165$		0			0
$166$	0.0743115	−	0.143924i	0.00576769	−	0.0111707i
$167$	8.50615	+	14.7331i	0.658226	+	1.14008i	0.981075	+	0.193630i	$0.0620261\pi$
$167$	8.50615	+	14.7331i	0.658226	+	1.14008i	−0.322849	+	0.946451i	$0.604641\pi$
$168$		0			0
$169$	−0.607170	+	1.05165i	−0.0467054	+	0.0808961i
$170$	−5.38871	−	8.39648i	−0.413295	−	0.643980i
$171$		0			0
$172$	6.08540	+	2.78827i	0.464008	+	0.212603i
$173$	−4.06899	−	2.34923i	−0.309360	−	0.178609i	0.337280	−	0.941404i	$-0.390493\pi$
$173$	−4.06899	−	2.34923i	−0.309360	−	0.178609i	−0.646640	+	0.762795i	$0.723826\pi$
$174$		0			0
$175$	−6.63546	−	9.82175i	−0.501594	−	0.742455i
$176$	15.9120	+	5.55156i	1.19941	+	0.418464i
$177$		0			0
$178$	0.240368	+	5.11286i	0.0180163	+	0.383225i
$179$		−	8.32224i		−	0.622034i	−0.950404	−	0.311017i	$-0.899330\pi$
$179$		−	8.32224i		−	0.622034i	0.950404	−	0.311017i	$-0.100670\pi$
$180$		0			0
$181$		−	9.07327i		−	0.674411i	−0.941431	−	0.337205i	$-0.890518\pi$
$181$		−	9.07327i		−	0.674411i	0.941431	−	0.337205i	$-0.109482\pi$
$182$	−1.50626	−	12.7566i	−0.111651	−	0.945581i
$183$		0			0
$184$	−12.0404	+	9.43239i	−0.887632	+	0.695365i
$185$	5.44320	−	3.14263i	0.400192	−	0.231051i
$186$		0			0
$187$	−4.82674	+	8.36015i	−0.352966	+	0.611355i
$188$	−3.67684	+	8.02473i	−0.268161	+	0.585263i
$189$		0			0
$190$	−6.26510	+	4.02083i	−0.454518	+	0.291702i
$191$	−10.1929	−	5.88490i	−0.737535	−	0.425816i	0.0836373	−	0.996496i	$-0.473346\pi$
$191$	−10.1929	−	5.88490i	−0.737535	−	0.425816i	−0.821172	+	0.570680i	$0.806680\pi$
$192$		0			0
$193$	10.6936	+	18.5218i	0.769742	+	1.33323i	0.937703	+	0.347438i	$0.112948\pi$
$193$	10.6936	+	18.5218i	0.769742	+	1.33323i	−0.167961	+	0.985794i	$0.553718\pi$
$194$	−8.03384	−	4.14806i	−0.576796	−	0.297813i
$195$		0			0
$196$	−9.63134	−	10.1606i	−0.687953	−	0.725756i
$197$	10.7855			0.768436			0.384218	−	0.923242i	$-0.374471\pi$
$197$	10.7855			0.768436			0.384218	+	0.923242i	$0.374471\pi$
$198$		0			0
$199$	4.64957			0.329599			0.164800	−	0.986327i	$-0.447302\pi$
$199$	4.64957			0.329599			0.164800	+	0.986327i	$0.447302\pi$
$200$	4.73147	−	11.7550i	0.334565	−	0.831205i
$201$		0			0
$202$	−21.5046	−	11.1033i	−1.51306	−	0.781227i
$203$	−14.1155	−	20.8937i	−0.990714	−	1.46645i
$204$		0			0
$205$	−7.88727	+	13.6612i	−0.550871	+	0.954137i
$206$	−1.23308	−	1.92134i	−0.0859130	−	0.133866i
$207$		0			0
$208$	10.4004	−	8.96676i	0.721136	−	0.621733i
$209$	6.23800	+	3.60151i	0.431491	+	0.249122i
$210$		0			0
$211$	−2.23918	+	1.29279i	−0.154151	+	0.0889993i	−0.575092	−	0.818089i	$-0.695034\pi$
$211$	−2.23918	+	1.29279i	−0.154151	+	0.0889993i	0.420940	+	0.907088i	$0.361700\pi$
$212$	−21.0554	+	1.98412i	−1.44609	+	0.136270i
$213$		0			0
$214$	−0.122440	−	2.60441i	−0.00836982	−	0.178034i
$215$	−10.3050			−0.702792
$216$		0			0
$217$	17.0102	−	1.20215i	1.15473	−	0.0816072i
$218$	−3.76971	+	0.177224i	−0.255317	+	0.0120031i
$219$		0			0
$220$	−25.8299	+	2.43404i	−1.74145	+	0.164103i
$221$	3.93299	+	6.81214i	0.264562	+	0.458234i
$222$		0			0
$223$	0.326746	−	0.565940i	0.0218805	−	0.0378981i	−0.854878	−	0.518829i	$-0.826368\pi$
$223$	0.326746	−	0.565940i	0.0218805	−	0.0378981i	0.876758	+	0.480931i	$0.159701\pi$
$224$	3.23920	−	14.6119i	0.216428	−	0.976299i
$225$		0			0
$226$	0.957371	+	1.49174i	0.0636833	+	0.0992289i
$227$	2.88313	−	4.99372i	0.191360	−	0.331445i	−0.754341	−	0.656483i	$-0.772044\pi$
$227$	2.88313	−	4.99372i	0.191360	−	0.331445i	0.945701	+	0.325037i	$0.105377\pi$
$228$		0			0
$229$	−24.2527	+	14.0023i	−1.60267	+	0.925299i	−0.611714	+	0.791079i	$0.709520\pi$
$229$	−24.2527	+	14.0023i	−1.60267	+	0.925299i	−0.990951	+	0.134220i	$0.957147\pi$
$230$	10.8027	−	20.9224i	0.712310	−	1.37958i
$231$		0			0
$232$	10.0652	−	25.0062i	0.660811	−	1.64174i
$233$	8.45031			0.553598			0.276799	−	0.960928i	$-0.410726\pi$
$233$	8.45031			0.553598			0.276799	+	0.960928i	$0.410726\pi$
$234$		0			0
$235$		−	13.5890i		−	0.886448i
$236$	−10.2976	−	14.4991i	−0.670316	−	0.943810i
$237$		0			0
$238$	7.87599	+	3.38638i	0.510525	+	0.219506i
$239$	18.5973	−	10.7371i	1.20296	−	0.694528i	0.241746	−	0.970339i	$-0.422280\pi$
$239$	18.5973	−	10.7371i	1.20296	−	0.694528i	0.961212	+	0.275811i	$0.0889465\pi$
$240$		0			0
$241$	−22.3544	−	12.9063i	−1.43998	−	0.831371i	−0.442129	−	0.896951i	$-0.645777\pi$
$241$	−22.3544	−	12.9063i	−1.43998	−	0.831371i	−0.997847	+	0.0655806i	$0.979110\pi$
$242$	5.15644	+	8.03455i	0.331468	+	0.516481i
$243$		0			0
$244$	−7.50339	−	3.43797i	−0.480355	−	0.220094i
$245$	19.9954	+	8.04417i	1.27746	+	0.513923i
$246$		0			0
$247$	5.08294	−	2.93464i	0.323420	−	0.186726i
$248$	11.2423	+	14.3508i	0.713887	+	0.911276i
$249$		0			0
$250$	−0.106319	−	2.26151i	−0.00672423	−	0.143031i
$251$	−14.3699			−0.907018			−0.453509	−	0.891252i	$-0.649828\pi$
$251$	−14.3699			−0.907018			−0.453509	+	0.891252i	$0.649828\pi$
$252$		0			0
$253$	−22.7833			−1.43237
$254$	0.708031	+	15.0605i	0.0444258	+	0.944979i
$255$		0			0
$256$	14.8833	−	5.87261i	0.930206	−	0.367038i
$257$	−14.8202	+	8.55644i	−0.924458	+	0.533736i	−0.885055	−	0.465487i	$-0.845879\pi$
$257$	−14.8202	+	8.55644i	−0.924458	+	0.533736i	−0.0394034	+	0.999223i	$0.512546\pi$
$258$		0			0
$259$	−2.36400	+	4.85607i	−0.146892	+	0.301741i
$260$	−8.80594	+	19.2190i	−0.546121	+	1.19191i
$261$		0			0
$262$	6.87888	+	10.7184i	0.424979	+	0.662185i
$263$	14.9410	+	8.62620i	0.921302	+	0.531914i	0.884050	−	0.467392i	$-0.154806\pi$
$263$	14.9410	+	8.62620i	0.921302	+	0.531914i	0.0372520	+	0.999306i	$0.488140\pi$
$264$		0			0
$265$	28.1962	−	16.2791i	1.73208	−	1.00001i
$266$	2.52677	−	5.87674i	0.154927	−	0.360326i
$267$		0			0
$268$	−17.9547	+	12.7518i	−1.09676	+	0.778942i
$269$		−	21.5478i		−	1.31379i	−0.753982	−	0.656895i	$-0.771869\pi$
$269$		−	21.5478i		−	1.31379i	0.753982	−	0.656895i	$-0.228131\pi$
$270$		0			0
$271$	−0.857294			−0.0520769			−0.0260384	−	0.999661i	$-0.508289\pi$
$271$	−0.857294			−0.0520769			−0.0260384	+	0.999661i	$0.508289\pi$
$272$	1.71211	+	9.00374i	0.103812	+	0.545932i
$273$		0			0
$274$	−1.44974	+	2.80781i	−0.0875818	+	0.169626i
$275$	16.3464	−	9.43758i	0.985723	−	0.569107i
$276$		0			0
$277$	8.94703	−	15.4967i	0.537575	−	0.931107i	−0.461459	−	0.887162i	$-0.652674\pi$
$277$	8.94703	−	15.4967i	0.537575	−	0.931107i	0.999034	−	0.0439457i	$-0.0139928\pi$
$278$	7.78830	+	12.1354i	0.467111	+	0.727834i
$279$		0			0
$280$	4.83664	+	22.5275i	0.289045	+	1.34628i
$281$	−10.8543	+	18.8002i	−0.647513	+	1.12153i	0.336202	+	0.941790i	$0.390857\pi$
$281$	−10.8543	+	18.8002i	−0.647513	+	1.12153i	−0.983715	+	0.179735i	$0.942476\pi$
$282$		0			0
$283$	11.7141	+	20.2894i	0.696331	+	1.20608i	0.969730	+	0.244180i	$0.0785186\pi$
$283$	11.7141	+	20.2894i	0.696331	+	1.20608i	−0.273399	+	0.961901i	$0.588148\pi$
$284$	0.466913	+	4.95487i	0.0277062	+	0.294017i
$285$		0			0
$286$	20.4324	−	0.960579i	1.20819	−	0.0568002i
$287$	−0.955580	−	13.5213i	−0.0564061	−	0.798138i
$288$		0			0
$289$	11.7501			0.691181
$290$	1.94878	+	41.4524i	0.114436	+	2.43417i
$291$		0			0
$292$	0.651058	+	6.90900i	0.0381003	+	0.404319i
$293$	−9.69068	+	5.59492i	−0.566136	+	0.326859i	−0.755605	−	0.655028i	$-0.772657\pi$
$293$	−9.69068	+	5.59492i	−0.566136	+	0.326859i	0.189469	+	0.981887i	$0.439323\pi$
$294$		0			0
$295$	23.7100	+	13.6889i	1.38045	+	0.797001i
$296$	−5.71658	+	0.811035i	−0.332269	+	0.0471405i
$297$		0			0
$298$	−9.42448	−	14.6849i	−0.545945	−	0.850671i
$299$	−9.28230	+	16.0774i	−0.536809	+	0.929781i
$300$		0			0
$301$	7.33748	−	4.95711i	0.422925	−	0.285723i
$302$	−13.5821	−	7.01275i	−0.781562	−	0.403539i
$303$		0			0
$304$	6.71822	−	1.27750i	0.385316	−	0.0732698i
$305$	12.7062			0.727553
$306$		0			0
$307$	9.18388			0.524152			0.262076	−	0.965047i	$-0.415593\pi$
$307$	9.18388			0.524152			0.262076	+	0.965047i	$0.415593\pi$
$308$	17.2209	−	14.1584i	0.981251	−	0.806748i
$309$		0			0
$310$	−24.9371	−	12.8756i	−1.41633	−	0.731284i
$311$	−3.81067	−	6.60027i	−0.216083	−	0.374267i	0.737524	−	0.675321i	$-0.235995\pi$
$311$	−3.81067	−	6.60027i	−0.216083	−	0.374267i	−0.953607	+	0.301054i	$0.902662\pi$
$312$		0			0
$313$	5.36993	+	3.10033i	0.303526	+	0.175241i	0.644026	−	0.765004i	$-0.277263\pi$
$313$	5.36993	+	3.10033i	0.303526	+	0.175241i	−0.340500	+	0.940245i	$0.610596\pi$
$314$	29.5282	−	18.9507i	1.66637	−	1.06945i
$315$		0			0
$316$	−18.6419	−	8.54149i	−1.04869	−	0.480496i
$317$	4.84502	−	8.39183i	0.272124	−	0.471332i	−0.697282	−	0.716797i	$-0.745607\pi$
$317$	4.84502	−	8.39183i	0.272124	−	0.471332i	0.969405	+	0.245465i	$0.0789407\pi$
$318$		0			0
$319$	34.7733	−	20.0764i	1.94693	−	1.12406i
$320$	−17.0643	+	17.7633i	−0.953922	+	0.992998i
$321$		0			0
$322$	2.37264	+	20.0940i	0.132222	+	1.11979i
$323$			3.91727i			0.217963i
$324$		0			0
$325$		−	15.3801i		−	0.853136i
$326$	0.725731	+	15.4370i	0.0401945	+	0.854975i
$327$		0			0
$328$	11.4073	−	8.93643i	0.629865	−	0.493432i
$329$	6.53686	+	9.67581i	0.360389	+	0.533445i
$330$		0			0
$331$	17.9174	+	10.3446i	0.984827	+	0.568590i	0.903724	−	0.428116i	$-0.140822\pi$
$331$	17.9174	+	10.3446i	0.984827	+	0.568590i	0.0811031	+	0.996706i	$0.474156\pi$
$332$	0.0954180	−	0.208250i	0.00523674	−	0.0114292i
$333$		0			0
$334$	12.9947	+	20.2478i	0.711038	+	1.10791i
$335$	16.9514	−	29.3608i	0.926157	−	1.60415i
$336$		0			0
$337$	8.28764	+	14.3546i	0.451457	+	0.781946i	0.998477	−	0.0551737i	$-0.0175713\pi$
$337$	8.28764	+	14.3546i	0.451457	+	0.781946i	−0.547020	+	0.837119i	$0.684238\pi$
$338$	−0.787879	+	1.52594i	−0.0428550	+	0.0830002i
$339$		0			0
$340$	−8.17001	−	11.5034i	−0.443081	−	0.623861i
$341$			27.1550i			1.47053i
$342$		0			0
$343$	−18.1069	+	3.89087i	−0.977683	+	0.210087i
$344$	8.78174	+	3.53471i	0.473480	+	0.190579i
$345$		0			0
$346$	−5.90410	−	3.04842i	−0.317406	−	0.163884i
$347$	−8.93889	+	5.16087i	−0.479865	+	0.277050i	−0.720360	−	0.693600i	$-0.756023\pi$
$347$	−8.93889	+	5.16087i	−0.479865	+	0.277050i	0.240495	+	0.970650i	$0.422690\pi$
$348$		0			0
$349$	−8.33414	−	4.81172i	−0.446116	−	0.257565i	0.260072	−	0.965589i	$-0.416254\pi$
$349$	−8.33414	−	4.81172i	−0.446116	−	0.257565i	−0.706189	+	0.708024i	$0.749587\pi$
$350$	−10.0259	−	13.4341i	−0.535906	−	0.718081i
$351$		0			0
$352$	22.8468	+	6.78567i	1.21774	+	0.361678i
$353$	−20.3278	−	11.7363i	−1.08194	−	0.624658i	−0.150520	−	0.988607i	$-0.548095\pi$
$353$	−20.3278	−	11.7363i	−1.08194	−	0.624658i	−0.931419	+	0.363949i	$0.881428\pi$
$354$		0			0
$355$	−3.83087	−	6.63526i	−0.203321	−	0.352163i
$356$	0.679114	+	7.20673i	0.0359929	+	0.381956i
$357$		0			0
$358$	−0.552700	−	11.7564i	−0.0292111	−	0.621347i
$359$		−	7.49888i		−	0.395776i	−0.980225	−	0.197888i	$-0.936592\pi$
$359$		−	7.49888i		−	0.395776i	0.980225	−	0.197888i	$-0.0634082\pi$
$360$		0			0
$361$	−16.0771			−0.846163
$362$	−0.602577	−	12.8174i	−0.0316708	−	0.673667i
$363$		0			0
$364$	−2.97502	−	17.9206i	−0.155933	−	0.939294i
$365$	−5.34171	−	9.25211i	−0.279598	−	0.484278i
$366$		0			0
$367$	−2.39341	+	4.14551i	−0.124935	+	0.216394i	−0.921708	−	0.387885i	$-0.873206\pi$
$367$	−2.39341	+	4.14551i	−0.124935	+	0.216394i	0.796772	+	0.604279i	$0.206539\pi$
$368$	−16.3825	+	14.1243i	−0.853998	+	0.736281i
$369$		0			0
$370$	7.48065	−	4.80095i	0.388900	−	0.249589i
$371$	−12.2457	+	25.1548i	−0.635765	+	1.30597i
$372$		0			0
$373$	−13.8959	−	24.0683i	−0.719500	−	1.24621i	−0.961198	−	0.275859i	$-0.911038\pi$
$373$	−13.8959	−	24.0683i	−0.719500	−	1.24621i	0.241698	−	0.970352i	$-0.422296\pi$
$374$	−6.26329	+	12.1306i	−0.323867	+	0.627256i
$375$		0			0
$376$	−4.66116	+	11.5803i	−0.240381	+	0.597211i
$377$		−	32.7179i		−	1.68506i
$378$		0			0
$379$		−	27.3958i		−	1.40723i	−0.710583	−	0.703613i	$-0.751569\pi$
$379$		−	27.3958i		−	1.40723i	0.710583	−	0.703613i	$-0.248431\pi$
$380$	−8.58338	+	6.09612i	−0.440318	+	0.312724i
$381$		0			0
$382$	−14.7899	−	7.63638i	−0.756718	−	0.390711i
$383$	7.36210	+	12.7515i	0.376185	+	0.651572i	0.990504	−	0.137486i	$-0.0439022\pi$
$383$	7.36210	+	12.7515i	0.376185	+	0.651572i	−0.614318	+	0.789058i	$0.710569\pi$
$384$		0			0
$385$	−15.0225	+	30.8588i	−0.765618	+	1.57271i
$386$	16.3364	+	25.4548i	0.831502	+	1.29561i
$387$		0			0
$388$	−11.6245	−	5.32622i	−0.590145	−	0.270398i
$389$	10.9505	−	18.9668i	0.555211	−	0.961653i	−0.442676	−	0.896681i	$-0.645971\pi$
$389$	10.9505	−	18.9668i	0.555211	−	0.961653i	0.997887	−	0.0649717i	$-0.0206957\pi$
$390$		0			0
$391$	−6.19520	−	10.7304i	−0.313305	−	0.542659i
$392$	−14.2805	−	13.7137i	−0.721276	−	0.692648i
$393$		0			0
$394$	15.2362	−	0.716291i	0.767588	−	0.0360862i
$395$	31.5679			1.58835
$396$		0			0
$397$			34.9584i			1.75451i	0.480025	+	0.877255i	$0.340628\pi$
$397$			34.9584i			1.75451i	−0.480025	+	0.877255i	$0.659372\pi$
$398$	6.56823	−	0.308789i	0.329236	−	0.0154782i
$399$		0			0
$400$	5.90324	−	16.9200i	0.295162	−	0.845999i
$401$	9.78297	+	16.9446i	0.488538	+	0.846173i	0.999913	−	0.0131845i	$-0.00419689\pi$
$401$	9.78297	+	16.9446i	0.488538	+	0.846173i	−0.511375	+	0.859358i	$0.670864\pi$
$402$		0			0
$403$	19.1624	+	11.0634i	0.954548	+	0.551109i
$404$	−31.1159	−	14.2570i	−1.54808	−	0.709311i
$405$		0			0
$406$	−21.3279	−	28.5780i	−1.05849	−	1.41830i
$407$	−7.44829	−	4.30027i	−0.369198	−	0.213156i
$408$		0			0
$409$	2.97407	−	1.71708i	0.147058	−	0.0849042i	−0.424665	−	0.905350i	$-0.639608\pi$
$409$	2.97407	−	1.71708i	0.147058	−	0.0849042i	0.571724	+	0.820446i	$0.306275\pi$
$410$	−10.2347	+	19.8223i	−0.505457	+	0.978953i
$411$		0			0
$412$	−1.86952	−	2.63230i	−0.0921047	−	0.129684i
$413$	−23.4672	+	1.65848i	−1.15475	+	0.0816084i
$414$		0			0
$415$			0.352649i			0.0173108i
$416$	14.0966	−	13.3576i	0.691143	−	0.654912i
$417$		0			0
$418$	9.05131	+	4.67340i	0.442714	+	0.228584i
$419$	−5.82364	−	10.0868i	−0.284503	−	0.492774i	0.687985	−	0.725725i	$-0.258495\pi$
$419$	−5.82364	−	10.0868i	−0.284503	−	0.492774i	−0.972489	+	0.232950i	$0.925162\pi$
$420$		0			0
$421$	−9.64312	+	16.7024i	−0.469977	+	0.814024i	−0.999411	−	0.0343274i	$-0.989071\pi$
$421$	−9.64312	+	16.7024i	−0.469977	+	0.814024i	0.529434	+	0.848351i	$0.322404\pi$
$422$	−3.07732	+	1.97497i	−0.149802	+	0.0961402i
$423$		0			0
$424$	−29.6123	+	4.20122i	−1.43810	+	0.204029i
$425$	8.88976	+	5.13251i	0.431217	+	0.248963i
$426$		0			0
$427$	−9.04721	+	6.11219i	−0.437825	+	0.295790i
$428$	−0.345930	−	3.67100i	−0.0167212	−	0.177444i
$429$		0			0
$430$	−14.5573	+	0.684377i	−0.702017	+	0.0330036i
$431$			1.73760i			0.0836971i	0.999124	+	0.0418485i	$0.0133247\pi$
$431$			1.73760i			0.0836971i	−0.999124	+	0.0418485i	$0.986675\pi$
$432$		0			0
$433$		−	5.95764i		−	0.286306i	−0.989701	−	0.143153i	$-0.954276\pi$
$433$		−	5.95764i		−	0.286306i	0.989701	−	0.143153i	$-0.0457241\pi$
$434$	23.9497	−	2.82791i	1.14962	−	0.135744i
$435$		0			0
$436$	−5.31353	+	0.500711i	−0.254472	+	0.0239797i
$437$	−8.00657	+	4.62260i	−0.383006	+	0.221129i
$438$		0			0
$439$	10.6377	−	18.4250i	0.507708	−	0.879377i	−0.492252	−	0.870453i	$-0.663826\pi$
$439$	10.6377	−	18.4250i	0.507708	−	0.879377i	0.999960	−	0.00892391i	$-0.00284061\pi$
$440$	−36.3271	+	5.15388i	−1.73182	+	0.245701i
$441$		0			0
$442$	6.00837	+	9.36200i	0.285789	+	0.445305i
$443$	30.1387	+	17.4006i	1.43193	+	0.826726i	0.997268	−	0.0738675i	$-0.0235342\pi$
$443$	30.1387	+	17.4006i	1.43193	+	0.826726i	0.434663	+	0.900593i	$0.356868\pi$
$444$		0			0
$445$	−5.57190	−	9.65081i	−0.264133	−	0.457492i
$446$	0.423993	−	0.821177i	0.0200766	−	0.0388838i
$447$		0			0
$448$	3.60546	−	20.8567i	0.170342	−	0.985385i
$449$	−0.109498			−0.00516755			−0.00258377	−	0.999997i	$-0.500822\pi$
$449$	−0.109498			−0.00516755			−0.00258377	+	0.999997i	$0.500822\pi$
$450$		0			0
$451$	21.5853			1.01641
$452$	1.45150	+	2.04373i	0.0682729	+	0.0961288i
$453$		0			0
$454$	3.74122	−	7.24588i	0.175584	−	0.340066i
$455$	15.6556	+	23.1733i	0.733947	+	1.08638i
$456$		0			0
$457$	14.6591	−	25.3902i	0.685722	−	1.18770i	−0.287488	−	0.957784i	$-0.592820\pi$
$457$	14.6591	−	25.3902i	0.685722	−	1.18770i	0.973209	−	0.229920i	$-0.0738466\pi$
$458$	−33.3308	+	21.3911i	−1.55744	+	0.999541i
$459$		0			0
$460$	13.8710	−	30.2735i	0.646738	−	1.41151i
$461$	28.8999	+	16.6853i	1.34600	+	0.777114i	0.987680	−	0.156485i	$-0.0500163\pi$
$461$	28.8999	+	16.6853i	1.34600	+	0.777114i	0.358320	+	0.933599i	$0.383350\pi$
$462$		0			0
$463$	−8.98085	+	5.18510i	−0.417376	+	0.240972i	−0.693954	−	0.720019i	$-0.744133\pi$
$463$	−8.98085	+	5.18510i	−0.417376	+	0.240972i	0.276578	+	0.960991i	$0.410800\pi$
$464$	12.5579	−	35.9936i	0.582984	−	1.67096i
$465$		0			0
$466$	11.9374	−	0.561205i	0.552988	−	0.0259973i
$467$	−7.81904			−0.361822			−0.180911	−	0.983499i	$-0.557905\pi$
$467$	−7.81904			−0.361822			−0.180911	+	0.983499i	$0.557905\pi$
$468$		0			0
$469$	2.05375	+	29.0602i	0.0948332	+	1.34188i
$470$	−0.902476	−	19.1965i	−0.0416281	−	0.885470i
$471$		0			0
$472$	−15.5098	−	19.7983i	−0.713898	−	0.911290i
$473$	7.05047	+	12.2118i	0.324181	+	0.561498i
$474$		0			0
$475$	3.82966	−	6.63317i	0.175717	−	0.304351i
$476$	11.3509	+	4.26072i	0.520270	+	0.195290i
$477$		0			0
$478$	25.5584	−	16.4030i	1.16902	−	0.750254i
$479$	2.78654	−	4.82643i	0.127320	−	0.220525i	−0.795317	−	0.606193i	$-0.792696\pi$
$479$	2.78654	−	4.82643i	0.127320	−	0.220525i	0.922638	+	0.385668i	$0.126029\pi$
$480$		0			0
$481$	−6.06912	+	3.50401i	−0.276728	+	0.159769i
$482$	−32.4362	−	16.7476i	−1.47743	−	0.762831i
$483$		0			0
$484$	7.81785	+	11.0076i	0.355357	+	0.500345i
$485$	19.6848			0.893842
$486$		0			0
$487$			22.6868i			1.02804i	0.857780	+	0.514018i	$0.171843\pi$
$487$			22.6868i			1.02804i	−0.857780	+	0.514018i	$0.828157\pi$
$488$	−10.8280	−	4.35834i	−0.490161	−	0.197293i
$489$		0			0
$490$	28.7807	+	10.0357i	1.30018	+	0.453366i
$491$	5.38821	−	3.11089i	0.243167	−	0.140392i	−0.373465	−	0.927644i	$-0.621830\pi$
$491$	5.38821	−	3.11089i	0.243167	−	0.140392i	0.616631	+	0.787252i	$0.288497\pi$
$492$		0			0
$493$	18.9110	+	10.9183i	0.851711	+	0.491735i
$494$	6.98553	−	4.48319i	0.314294	−	0.201708i
$495$		0			0
$496$	16.8346	+	19.5261i	0.755894	+	0.876746i
$497$	5.91954	+	2.88172i	0.265528	+	0.129263i
$498$		0			0
$499$	35.4214	−	20.4505i	1.58568	−	0.915491i	0.591670	−	0.806180i	$-0.298469\pi$
$499$	35.4214	−	20.4505i	1.58568	−	0.915491i	0.994008	−	0.109311i	$-0.0348645\pi$
$500$	−0.300385	−	3.18768i	−0.0134336	−	0.142557i
$501$		0			0
$502$	−20.2996	+	0.954337i	−0.906017	+	0.0425941i
$503$	−8.58006			−0.382566			−0.191283	−	0.981535i	$-0.561265\pi$
$503$	−8.58006			−0.382566			−0.191283	+	0.981535i	$0.561265\pi$
$504$		0			0
$505$	52.6914			2.34474
$506$	−32.1849	+	1.51309i	−1.43079	+	0.0672651i
$507$		0			0
$508$	2.00040	+	21.2282i	0.0887536	+	0.941850i
$509$	5.48332	−	3.16579i	0.243044	−	0.140321i	−0.373531	−	0.927618i	$-0.621853\pi$
$509$	5.48332	−	3.16579i	0.243044	−	0.140321i	0.616575	+	0.787296i	$0.288520\pi$
$510$		0			0
$511$	8.25413	+	4.01823i	0.365141	+	0.177756i
$512$	20.6349	−	9.28440i	0.911943	−	0.410317i
$513$		0			0
$514$	−20.3675	+	13.0715i	−0.898373	+	0.576560i
$515$	4.30453	+	2.48522i	0.189680	+	0.109512i
$516$		0			0
$517$	−16.1035	+	9.29734i	−0.708230	+	0.408897i
$518$	−3.01702	+	7.01694i	−0.132560	+	0.308306i
$519$		0			0
$520$	−11.1634	+	27.7346i	−0.489546	+	1.21624i
$521$		−	19.8412i		−	0.869261i	−0.900609	−	0.434630i	$-0.856879\pi$
$521$		−	19.8412i		−	0.869261i	0.900609	−	0.434630i	$-0.143121\pi$
$522$		0			0
$523$	−39.5715			−1.73034			−0.865171	−	0.501476i	$-0.832790\pi$
$523$	−39.5715			−1.73034			−0.865171	+	0.501476i	$0.832790\pi$
$524$	10.4293	+	14.6845i	0.455606	+	0.641497i
$525$		0			0
$526$	21.6794	+	11.1936i	0.945265	+	0.488062i
$527$	−12.7894	+	7.38396i	−0.557114	+	0.321650i
$528$		0			0
$529$	3.12136	−	5.40635i	0.135711	−	0.235059i
$530$	38.7503	−	24.8692i	1.68320	−	1.08025i
$531$		0			0
$532$	3.17917	−	8.46960i	0.137834	−	0.367204i
$533$	8.79424	−	15.2321i	0.380921	−	0.659774i
$534$		0			0
$535$	2.83824	+	4.91598i	0.122708	+	0.212536i
$536$	−24.5168	+	19.2063i	−1.05897	+	0.829587i
$537$		0			0
$538$	−1.43104	−	30.4395i	−0.0616964	−	1.31234i
$539$	−4.14782	−	29.1989i	−0.178659	−	1.25769i
$540$		0			0
$541$	−14.8643			−0.639068			−0.319534	−	0.947575i	$-0.603526\pi$
$541$	−14.8643			−0.639068			−0.319534	+	0.947575i	$0.603526\pi$
$542$	−1.21106	+	0.0569349i	−0.0520194	+	0.00244556i
$543$		0			0
$544$	3.01657	+	12.6055i	0.129335	+	0.540455i
$545$	7.11556	−	4.10817i	0.304797	−	0.175975i
$546$		0			0
$547$	−17.5001	−	10.1037i	−0.748252	−	0.432003i	0.0768102	−	0.997046i	$-0.475526\pi$
$547$	−17.5001	−	10.1037i	−0.748252	−	0.432003i	−0.825062	+	0.565042i	$0.808860\pi$
$548$	−1.86150	+	4.06274i	−0.0795194	+	0.173552i
$549$		0			0
$550$	22.4650	−	14.4176i	0.957910	−	0.614770i
$551$	8.14678	−	14.1106i	0.347064	−	0.601133i
$552$		0			0
$553$	−22.4774	+	15.1855i	−0.955837	+	0.645752i
$554$	11.6099	−	22.4857i	0.493257	−	0.955325i
$555$		0			0
$556$	11.8081	+	16.6259i	0.500775	+	0.705095i
$557$	−12.0437			−0.510308			−0.255154	−	0.966900i	$-0.582126\pi$
$557$	−12.0437			−0.510308			−0.255154	+	0.966900i	$0.582126\pi$
$558$		0			0
$559$	11.4899			0.485973
$560$	8.32860	+	31.5024i	0.351948	+	1.33122i
$561$		0			0
$562$	−14.0848	+	27.2790i	−0.594131	+	1.15070i
$563$	19.3253	+	33.4724i	0.814463	+	1.41069i	0.909713	+	0.415238i	$0.136302\pi$
$563$	19.3253	+	33.4724i	0.814463	+	1.41069i	−0.0952496	+	0.995453i	$0.530365\pi$
$564$		0			0
$565$	−3.34205	−	1.92953i	−0.140601	−	0.0811761i
$566$	17.8954	+	27.8839i	0.752201	+	1.17205i
$567$		0			0
$568$	0.988651	+	6.96850i	0.0414829	+	0.292392i
$569$	6.96304	−	12.0603i	0.291906	−	0.505596i	−0.682355	−	0.731021i	$-0.739044\pi$
$569$	6.96304	−	12.0603i	0.291906	−	0.505596i	0.974260	+	0.225426i	$0.0723773\pi$
$570$		0			0
$571$	−21.6359	+	12.4915i	−0.905436	+	0.522754i	−0.878960	−	0.476896i	$-0.841762\pi$
$571$	−21.6359	+	12.4915i	−0.905436	+	0.522754i	−0.0264762	+	0.999649i	$0.508429\pi$
$572$	28.8001	−	2.71393i	1.20419	−	0.113475i
$573$		0			0
$574$	−2.24788	−	19.0375i	−0.0938249	−	0.794608i
$575$			24.2266i			1.01032i
$576$		0			0
$577$		−	41.9153i		−	1.74495i	−0.488654	−	0.872477i	$-0.662512\pi$
$577$		−	41.9153i		−	1.74495i	0.488654	−	0.872477i	$-0.337488\pi$
$578$	16.5988	−	0.780351i	0.690419	−	0.0324583i
$579$		0			0
$580$	5.50590	+	58.4284i	0.228620	+	2.42611i
$581$	−0.169639	−	0.251098i	−0.00703780	−	0.0104173i
$582$		0			0
$583$	−38.5826	−	22.2757i	−1.59793	−	0.922565i
$584$	1.37856	+	9.71678i	0.0570453	+	0.402083i
$585$		0			0
$586$	−13.3180	+	8.54726i	−0.550162	+	0.353084i
$587$	13.1495	−	22.7757i	0.542740	−	0.940053i	−0.456006	−	0.889977i	$-0.650720\pi$
$587$	13.1495	−	22.7757i	0.542740	−	0.940053i	0.998745	−	0.0500760i	$-0.0159464\pi$
$588$		0			0
$589$	5.50960	+	9.54291i	0.227019	+	0.393209i
$590$	34.4031	+	17.7631i	1.41635	+	0.731295i
$591$		0			0
$592$	−8.02168	+	1.52536i	−0.329689	+	0.0626920i
$593$		−	14.9954i		−	0.615786i	−0.951421	−	0.307893i	$-0.900376\pi$
$593$		−	14.9954i		−	0.615786i	0.951421	−	0.307893i	$-0.0996239\pi$
$594$		0			0
$595$	−18.6187	+	1.31582i	−0.763291	+	0.0539434i
$596$	−14.2888	−	20.1187i	−0.585291	−	0.824094i
$597$		0			0
$598$	−12.0449	+	23.3283i	−0.492554	+	0.953964i
$599$	−11.6301	+	6.71463i	−0.475192	+	0.274352i	−0.718411	−	0.695619i	$-0.755130\pi$
$599$	−11.6301	+	6.71463i	−0.475192	+	0.274352i	0.243219	+	0.969972i	$0.421797\pi$
$600$		0			0
$601$	11.6714	+	6.73847i	0.476086	+	0.274868i	0.718784	−	0.695234i	$-0.244699\pi$
$601$	11.6714	+	6.73847i	0.476086	+	0.274868i	−0.242698	+	0.970102i	$0.578032\pi$
$602$	10.0361	−	7.48998i	0.409041	−	0.305269i
$603$		0			0
$604$	−19.6525	−	9.00457i	−0.799650	−	0.366391i
$605$	−18.0004	−	10.3925i	−0.731821	−	0.422517i
$606$		0			0
$607$	17.3550	+	30.0598i	0.704419	+	1.22009i	0.966901	+	0.255153i	$0.0821257\pi$
$607$	17.3550	+	30.0598i	0.704419	+	1.22009i	−0.262482	+	0.964937i	$0.584541\pi$
$608$	9.40567	−	2.25084i	0.381450	−	0.0912837i
$609$		0			0
$610$	17.9494	−	0.843846i	0.726750	−	0.0341663i
$611$			15.1516i			0.612968i
$612$		0			0
$613$	−27.2426			−1.10032			−0.550159	−	0.835060i	$-0.685433\pi$
$613$	−27.2426			−1.10032			−0.550159	+	0.835060i	$0.685433\pi$
$614$	12.9736	−	0.609923i	0.523573	−	0.0246145i
$615$		0			0
$616$	23.3869	−	21.1446i	0.942283	−	0.851938i
$617$	3.19357	+	5.53142i	0.128568	+	0.222687i	0.923122	−	0.384507i	$-0.125629\pi$
$617$	3.19357	+	5.53142i	0.128568	+	0.222687i	−0.794554	+	0.607194i	$0.792295\pi$
$618$		0			0
$619$	−13.4240	+	23.2510i	−0.539554	+	0.934536i	0.459374	+	0.888243i	$0.348074\pi$
$619$	−13.4240	+	23.2510i	−0.539554	+	0.934536i	−0.998928	+	0.0462924i	$0.985259\pi$
$620$	−36.0825	−	16.5326i	−1.44911	−	0.663966i
$621$		0			0
$622$	−5.82149	−	9.07082i	−0.233421	−	0.363707i
$623$	8.60982	+	4.19139i	0.344945	+	0.167924i
$624$		0			0
$625$	13.6647	+	23.6679i	0.546588	+	0.946718i
$626$	7.79175	+	4.02306i	0.311421	+	0.160794i
$627$		0			0
$628$	40.4545	−	28.7318i	1.61431	−	1.14652i
$629$		−	4.67729i		−	0.186496i
$630$		0			0
$631$		−	24.9328i		−	0.992557i	−0.868163	−	0.496279i	$-0.834699\pi$
$631$		−	24.9328i		−	0.992557i	0.868163	−	0.496279i	$-0.165301\pi$
$632$	−26.9017	−	10.8281i	−1.07009	−	0.430719i
$633$		0			0
$634$	6.28702	−	12.1765i	0.249689	−	0.483591i
$635$	−16.4126	−	28.4275i	−0.651316	−	1.12811i
$636$		0			0
$637$	−22.2946	−	8.96918i	−0.883346	−	0.355372i
$638$	47.7894	−	30.6704i	1.89200	−	1.21425i
$639$		0			0
$640$	−22.9262	+	26.2266i	−0.906237	+	1.03670i
$641$	−12.1458	+	21.0372i	−0.479732	+	0.830920i	−0.999730	−	0.0232475i	$-0.992599\pi$
$641$	−12.1458	+	21.0372i	−0.479732	+	0.830920i	0.519998	+	0.854168i	$0.325933\pi$
$642$		0			0
$643$	−5.13144	−	8.88791i	−0.202364	−	0.350505i	0.746926	−	0.664908i	$-0.231529\pi$
$643$	−5.13144	−	8.88791i	−0.202364	−	0.350505i	−0.949290	+	0.314403i	$0.898196\pi$
$644$	4.68620	+	28.2283i	0.184662	+	1.11235i
$645$		0			0
$646$	0.260155	+	5.53374i	0.0102357	+	0.217722i
$647$	−44.3871			−1.74504			−0.872518	−	0.488581i	$-0.837515\pi$
$647$	−44.3871			−1.74504			−0.872518	+	0.488581i	$0.837515\pi$
$648$		0			0
$649$		−	37.4629i		−	1.47055i
$650$	−1.02143	−	21.7268i	−0.0400638	−	0.852195i
$651$		0			0
$652$	2.05041	+	21.7589i	0.0803004	+	0.852145i
$653$	−11.3840	−	19.7176i	−0.445489	−	0.771610i	0.552597	−	0.833449i	$-0.313637\pi$
$653$	−11.3840	−	19.7176i	−0.445489	−	0.771610i	−0.998086	+	0.0618385i	$0.980304\pi$
$654$		0			0
$655$	−24.0132	−	13.8640i	−0.938274	−	0.541713i
$656$	15.5211	−	13.3817i	0.605998	−	0.522466i
$657$		0			0
$658$	9.87692	+	13.2344i	0.385042	+	0.515932i
$659$	−20.9713	−	12.1078i	−0.816927	−	0.471653i	0.0324284	−	0.999474i	$-0.489676\pi$
$659$	−20.9713	−	12.1078i	−0.816927	−	0.471653i	−0.849356	+	0.527821i	$0.823009\pi$
$660$		0			0
$661$	9.97746	−	5.76049i	0.388078	−	0.224057i	−0.293249	−	0.956036i	$-0.594736\pi$
$661$	9.97746	−	5.76049i	0.388078	−	0.224057i	0.681327	+	0.731979i	$0.261403\pi$
$662$	25.9980	+	13.4234i	1.01044	+	0.521715i
$663$		0			0
$664$	0.120962	−	0.300522i	0.00469424	−	0.0116625i
$665$	0.981811	+	13.8925i	0.0380730	+	0.538727i
$666$		0			0
$667$			51.5368i			1.99551i
$668$	19.7017	+	27.7402i	0.762282	+	1.07330i
$669$		0			0
$670$	21.9966	−	42.6024i	0.849803	−	1.64587i
$671$	−8.69333	−	15.0573i	−0.335602	−	0.581280i
$672$		0			0
$673$	10.9799	−	19.0178i	0.423245	−	0.733083i	−0.573009	−	0.819549i	$-0.694224\pi$
$673$	10.9799	−	19.0178i	0.423245	−	0.733083i	0.996255	+	0.0864662i	$0.0275575\pi$
$674$	12.6609	+	19.7277i	0.487679	+	0.759882i
$675$		0			0
$676$	−1.01166	+	2.20795i	−0.0389099	+	0.0849211i
$677$	38.3056	+	22.1157i	1.47220	+	0.849977i	0.999512	−	0.0312511i	$-0.00994916\pi$
$677$	38.3056	+	22.1157i	1.47220	+	0.849977i	0.472692	+	0.881228i	$0.343282\pi$
$678$		0			0
$679$	−14.0162	+	9.46921i	−0.537894	+	0.363395i
$680$	−12.3054	−	15.7078i	−0.471889	−	0.602366i
$681$		0			0
$682$	1.80343	+	38.3606i	0.0690568	+	1.46890i
$683$		−	15.0761i		−	0.576872i	−0.957499	−	0.288436i	$-0.906865\pi$
$683$		−	15.0761i		−	0.576872i	0.957499	−	0.288436i	$-0.0931352\pi$
$684$		0			0
$685$		−	6.87980i		−	0.262864i
$686$	−25.3204	+	6.69898i	−0.966738	+	0.255768i
$687$		0			0
$688$	12.6403	+	4.41010i	0.481907	+	0.168133i
$689$	−31.4385	+	18.1510i	−1.19771	+	0.691499i
$690$		0			0
$691$	11.3171	−	19.6017i	0.430522	−	0.745686i	−0.566396	−	0.824133i	$-0.691663\pi$
$691$	11.3171	−	19.6017i	0.430522	−	0.745686i	0.996918	+	0.0784473i	$0.0249962\pi$
$692$	−8.54289	−	3.91426i	−0.324752	−	0.148798i
$693$		0			0
$694$	−12.2848	+	7.88418i	−0.466325	+	0.299279i
$695$	−27.1879	−	15.6969i	−1.03130	−	0.595418i
$696$		0			0
$697$	5.86946	+	10.1662i	0.222321	+	0.385072i
$698$	−12.0928	−	6.24380i	−0.457720	−	0.236331i
$699$		0			0
$700$	−15.0553	−	18.3118i	−0.569037	−	0.692122i
$701$	−8.62984			−0.325945			−0.162972	−	0.986631i	$-0.552108\pi$
$701$	−8.62984			−0.325945			−0.162972	+	0.986631i	$0.552108\pi$
$702$		0			0
$703$	−3.49000			−0.131628
$704$	32.7252	+	8.06849i	1.23338	+	0.304093i
$705$		0			0
$706$	−29.4955	−	15.2292i	−1.11008	−	0.573160i
$707$	−37.5180	+	25.3467i	−1.41101	+	0.953262i
$708$		0			0
$709$	11.8717	−	20.5624i	0.445851	−	0.772237i	−0.552260	−	0.833672i	$-0.686234\pi$
$709$	11.8717	−	20.5624i	0.445851	−	0.772237i	0.998111	+	0.0614349i	$0.0195677\pi$
$710$	−5.85235	−	9.11890i	−0.219635	−	0.342226i
$711$		0			0
$712$	1.43797	+	10.1355i	0.0538901	+	0.379844i
$713$	−30.1844	−	17.4270i	−1.13041	−	0.652645i
$714$		0			0
$715$	−38.5674	+	22.2669i	−1.44234	+	0.832735i
$716$	−1.56155	−	16.5711i	−0.0583577	−	0.619290i
$717$		0			0
$718$	−0.498018	−	10.5933i	−0.0185859	−	0.395339i
$719$	−25.3519			−0.945467			−0.472734	−	0.881205i	$-0.656733\pi$
$719$	−25.3519			−0.945467			−0.472734	+	0.881205i	$0.656733\pi$
$720$		0			0
$721$	−4.26046	+	0.301096i	−0.158668	+	0.0112134i
$722$	−22.7114	+	1.06772i	−0.845229	+	0.0397363i
$723$		0			0
$724$	−1.70247	−	18.0665i	−0.0632716	−	0.671436i
$725$	−21.3482	−	36.9762i	−0.792853	−	1.37326i
$726$		0			0
$727$	5.16319	−	8.94291i	0.191492	−	0.331674i	−0.754253	−	0.656584i	$-0.772001\pi$
$727$	5.16319	−	8.94291i	0.191492	−	0.331674i	0.945745	+	0.324910i	$0.105334\pi$
$728$	−5.39281	−	25.1180i	−0.199871	−	0.930935i
$729$		0			0
$730$	−8.16044	−	12.7153i	−0.302031	−	0.470613i
$731$	−3.83431	+	6.64122i	−0.141817	+	0.245634i
$732$		0			0
$733$	10.1555	−	5.86329i	0.375102	−	0.216565i	−0.300583	−	0.953756i	$-0.597181\pi$
$733$	10.1555	−	5.86329i	0.375102	−	0.216565i	0.675685	+	0.737190i	$0.263848\pi$
$734$	−3.10575	+	6.01512i	−0.114635	+	0.222022i
$735$		0			0
$736$	−22.2048	+	21.0408i	−0.818479	+	0.775573i
$737$	−46.3915			−1.70885
$738$		0			0
$739$		−	0.463561i		−	0.0170524i	−0.999964	−	0.00852618i	$-0.997286\pi$
$739$		−	0.463561i		−	0.0170524i	0.999964	−	0.00852618i	$-0.00271400\pi$
$740$	10.2487	−	7.27888i	0.376750	−	0.267577i
$741$		0			0
$742$	−15.6284	+	36.3482i	−0.573735	+	1.33438i
$743$	11.4461	−	6.60840i	0.419916	−	0.242439i	−0.275125	−	0.961408i	$-0.588719\pi$
$743$	11.4461	−	6.60840i	0.419916	−	0.242439i	0.695041	+	0.718970i	$0.255386\pi$
$744$		0			0
$745$	32.8996	+	18.9946i	1.20535	+	0.695907i
$746$	−21.2285	−	33.0773i	−0.777229	−	1.21105i
$747$		0			0
$748$	−8.04224	+	17.5522i	−0.294053	+	0.641773i
$749$	−4.38571	−	2.13503i	−0.160250	−	0.0780123i
$750$		0			0
$751$	−9.82352	+	5.67161i	−0.358465	+	0.206960i	−0.668407	−	0.743795i	$-0.733024\pi$
$751$	−9.82352	+	5.67161i	−0.358465	+	0.206960i	0.309942	+	0.950755i	$0.399690\pi$
$752$	−5.81553	+	16.6686i	−0.212070	+	0.607840i
$753$		0			0
$754$	−2.17287	−	46.2191i	−0.0791314	−	1.68320i
$755$	33.2794			1.21116
$756$		0			0
$757$	−21.1566			−0.768950			−0.384475	−	0.923135i	$-0.625618\pi$
$757$	−21.1566			−0.768950			−0.384475	+	0.923135i	$0.625618\pi$
$758$	−1.81942	−	38.7007i	−0.0660842	−	1.40567i
$759$		0			0
$760$	−11.7205	+	9.18175i	−0.425147	+	0.333057i
$761$	−7.75469	+	4.47717i	−0.281107	+	0.162297i	−0.633925	−	0.773395i	$-0.718557\pi$
$761$	−7.75469	+	4.47717i	−0.281107	+	0.162297i	0.352817	+	0.935692i	$0.385224\pi$
$762$		0			0
$763$	−3.09032	+	6.34803i	−0.111877	+	0.229814i
$764$	−21.4002	−	9.80532i	−0.774231	−	0.354744i
$765$		0			0
$766$	11.2469	+	17.5245i	0.406369	+	0.633188i
$767$	−26.4364	−	15.2631i	−0.954563	−	0.551117i
$768$		0			0
$769$	−7.27639	+	4.20103i	−0.262393	+	0.151493i	−0.625426	−	0.780284i	$-0.715075\pi$
$769$	−7.27639	+	4.20103i	−0.262393	+	0.151493i	0.363033	+	0.931776i	$0.381741\pi$
$770$	−19.1722	+	44.5904i	−0.690918	+	1.60693i
$771$		0			0
$772$	24.7682	+	34.8738i	0.891427	+	1.25514i
$773$			5.75834i			0.207113i	0.994624	+	0.103556i	$0.0330223\pi$
$773$			5.75834i			0.207113i	−0.994624	+	0.103556i	$0.966978\pi$
$774$		0			0
$775$	28.8753			1.03723
$776$	−16.7751	−	6.75209i	−0.602192	−	0.242386i
$777$		0			0
$778$	14.2096	−	27.5207i	0.509438	−	0.986665i
$779$	7.58559	−	4.37954i	0.271782	−	0.156913i
$780$		0			0
$781$	−5.24202	+	9.07945i	−0.187574	+	0.324888i
$782$	−9.46430	−	14.7469i	−0.338443	−	0.527348i
$783$		0			0
$784$	−21.0842	−	18.4244i	−0.753007	−	0.658013i
$785$	−38.1942	+	66.1542i	−1.36321	+	2.36115i
$786$		0			0
$787$	−18.4924	−	32.0297i	−0.659181	−	1.14174i	−0.980828	−	0.194876i	$-0.937570\pi$
$787$	−18.4924	−	32.0297i	−0.659181	−	1.14174i	0.321647	−	0.946860i	$-0.395764\pi$
$788$	21.4759	−	2.02374i	0.765047	−	0.0720928i
$789$		0			0
$790$	44.5945	−	2.09650i	1.58660	−	0.0745901i
$791$	3.30784	−	0.233772i	0.117613	−	0.00831197i
$792$		0			0
$793$	−14.1673			−0.503094
$794$	2.32167	+	49.3841i	0.0823929	+	1.75257i
$795$		0			0
$796$	9.25812	−	0.872423i	0.328145	−	0.0309222i
$797$	−20.0024	+	11.5484i	−0.708522	+	0.409065i	−0.810513	−	0.585720i	$-0.800812\pi$
$797$	−20.0024	+	11.5484i	−0.708522	+	0.409065i	0.101992	+	0.994785i	$0.467478\pi$
$798$		0			0
$799$	−8.75767	−	5.05624i	−0.309824	−	0.178877i
$800$	7.21554	−	24.2941i	0.255108	−	0.858927i
$801$		0			0
$802$	14.9453	+	23.2871i	0.527736	+	0.822298i
$803$	−7.30941	+	12.6603i	−0.257943	+	0.446771i
$804$		0			0
$805$	−24.6605	−	36.5023i	−0.869169	−	1.28654i
$806$	27.8046	+	14.3562i	0.979375	+	0.505674i
$807$		0			0
$808$	−44.9029	−	18.0737i	−1.57968	−	0.635830i
$809$	22.9976			0.808553			0.404277	−	0.914637i	$-0.367523\pi$
$809$	22.9976			0.808553			0.404277	+	0.914637i	$0.367523\pi$
$810$		0			0
$811$	27.1173			0.952216			0.476108	−	0.879387i	$-0.342047\pi$
$811$	27.1173			0.952216			0.476108	+	0.879387i	$0.342047\pi$
$812$	−32.0269	−	38.9544i	−1.12392	−	1.36703i
$813$		0			0
$814$	−10.8074	−	5.58013i	−0.378800	−	0.195584i
$815$	−16.8230	−	29.1382i	−0.589282	−	1.02067i
$816$		0			0
$817$	4.95540	+	2.86100i	0.173368	+	0.100094i
$818$	4.08730	−	2.62315i	0.142909	−	0.0917165i
$819$		0			0
$820$	−13.1417	+	28.6817i	−0.458927	+	1.00161i
$821$	2.27415	−	3.93894i	0.0793682	−	0.137470i	−0.823609	−	0.567158i	$-0.808043\pi$
$821$	2.27415	−	3.93894i	0.0793682	−	0.137470i	0.902978	+	0.429688i	$0.141376\pi$
$822$		0			0
$823$	−20.0197	+	11.5584i	−0.697844	+	0.402900i	−0.806544	−	0.591174i	$-0.798665\pi$
$823$	−20.0197	+	11.5584i	−0.697844	+	0.402900i	0.108700	+	0.994075i	$0.465331\pi$
$824$	−2.81580	−	3.59437i	−0.0980931	−	0.125216i
$825$		0			0
$826$	−33.0409	+	3.90137i	−1.14964	+	0.135746i
$827$			51.8058i			1.80146i	0.434376	+	0.900732i	$0.356969\pi$
$827$			51.8058i			1.80146i	−0.434376	+	0.900732i	$0.643031\pi$
$828$		0			0
$829$		−	13.9412i		−	0.484197i	−0.970252	−	0.242098i	$-0.922164\pi$
$829$		−	13.9412i		−	0.484197i	0.970252	−	0.242098i	$-0.0778357\pi$
$830$	0.0234202	+	0.498170i	0.000812928	+	0.0172917i
$831$		0			0
$832$	19.0265	−	19.8059i	0.659626	−	0.686646i
$833$	12.6242	−	9.89326i	0.437401	−	0.342781i
$834$		0			0
$835$	−45.3627	−	26.1902i	−1.56984	−	0.906349i
$836$	13.0967	+	6.00078i	0.452960	+	0.207541i
$837$		0			0
$838$	−8.89667	−	13.8624i	−0.307330	−	0.478870i
$839$	−24.6769	+	42.7416i	−0.851941	+	1.47561i	0.0275127	+	0.999621i	$0.491241\pi$
$839$	−24.6769	+	42.7416i	−0.851941	+	1.47561i	−0.879454	+	0.475984i	$0.842092\pi$
$840$		0			0
$841$	−30.9137	−	53.5441i	−1.06599	−	1.84635i
$842$	−12.5131	+	24.2351i	−0.431231	+	0.835196i
$843$		0			0
$844$	−4.21603	+	2.99432i	−0.145122	+	0.103069i
$845$		−	3.73892i		−	0.128623i
$846$		0			0
$847$	17.8161	−	1.25910i	0.612170	−	0.0432633i
$848$	−41.5528	+	7.90148i	−1.42693	+	0.271338i
$849$		0			0
$850$	12.8990	+	6.66006i	0.442433	+	0.228438i
$851$	9.56000	−	5.51947i	0.327713	−	0.189205i
$852$		0			0
$853$	24.2685	+	14.0114i	0.830939	+	0.479743i	0.854174	−	0.519987i	$-0.174063\pi$
$853$	24.2685	+	14.0114i	0.830939	+	0.479743i	−0.0232350	+	0.999730i	$0.507397\pi$
$854$	−12.3746	+	9.23525i	−0.423452	+	0.316024i
$855$		0			0
$856$	−0.732479	−	5.16288i	−0.0250356	−	0.176463i
$857$	9.87736	+	5.70269i	0.337404	+	0.194800i	0.659123	−	0.752035i	$-0.270927\pi$
$857$	9.87736	+	5.70269i	0.337404	+	0.194800i	−0.321719	+	0.946835i	$0.604261\pi$
$858$		0			0
$859$	−20.0438	−	34.7168i	−0.683884	−	1.18452i	−0.973786	−	0.227466i	$-0.926956\pi$
$859$	−20.0438	−	34.7168i	−0.683884	−	1.18452i	0.289902	−	0.957056i	$-0.406377\pi$
$860$	−20.5190	+	1.93357i	−0.699693	+	0.0659343i
$861$		0			0
$862$	0.115398	+	2.45462i	0.00393047	+	0.0836047i
$863$			45.2430i			1.54009i	0.637989	+	0.770045i	$0.279766\pi$
$863$			45.2430i			1.54009i	−0.637989	+	0.770045i	$0.720234\pi$
$864$		0			0
$865$	14.4664			0.491874
$866$	−0.395661	−	8.41609i	−0.0134451	−	0.285990i
$867$		0			0
$868$	33.6448	−	5.58541i	1.14198	−	0.189581i
$869$	−21.5982	−	37.4092i	−0.732669	−	1.26902i
$870$		0			0
$871$	−18.9007	+	32.7370i	−0.640426	+	1.10925i
$872$	−7.47292	+	1.06022i	−0.253065	+	0.0359034i
$873$		0			0
$874$	−11.0035	+	7.06186i	−0.372199	+	0.238871i
$875$	−3.80829	−	1.85393i	−0.128744	−	0.0626743i
$876$		0			0
$877$	6.89651	+	11.9451i	0.232878	+	0.403357i	0.958654	−	0.284574i	$-0.0918522\pi$
$877$	6.89651	+	11.9451i	0.232878	+	0.403357i	−0.725776	+	0.687932i	$0.758519\pi$
$878$	13.8037	−	26.7346i	0.465852	−	0.902249i
$879$		0			0
$880$	−50.9753	+	9.69320i	−1.71838	+	0.326758i
$881$			46.4443i			1.56475i	0.622808	+	0.782375i	$0.285992\pi$
$881$			46.4443i			1.56475i	−0.622808	+	0.782375i	$0.714008\pi$
$882$		0			0
$883$		−	22.9737i		−	0.773127i	−0.922263	−	0.386564i	$-0.873662\pi$
$883$		−	22.9737i		−	0.773127i	0.922263	−	0.386564i	$-0.126338\pi$
$884$	9.10949	+	12.8262i	0.306385	+	0.431393i
$885$		0			0
$886$	43.7311	+	22.5794i	1.46917	+	0.758569i
$887$	10.6026	+	18.3642i	0.356000	+	0.616610i	0.987289	−	0.158938i	$-0.0508071\pi$
$887$	10.6026	+	18.3642i	0.356000	+	0.616610i	−0.631289	+	0.775548i	$0.717474\pi$
$888$		0			0
$889$	25.3612	+	12.3462i	0.850586	+	0.414078i
$890$	−8.51210	−	13.2632i	−0.285326	−	0.444584i
$891$		0			0
$892$	0.544418	−	1.18820i	0.0182285	−	0.0397838i
$893$	−3.77276	+	6.53461i	−0.126251	+	0.218672i
$894$		0			0
$895$	12.8120	+	22.1910i	0.428257	+	0.741763i
$896$	3.70812	−	29.7027i	0.123880	−	0.992297i
$897$		0			0
$898$	−0.154683	+	0.00727204i	−0.00516184	+	0.000242671i
$899$	61.4259			2.04867
$900$		0			0
$901$		−	24.2287i		−	0.807175i
$902$	30.4926	−	1.43353i	1.01529	−	0.0477314i
$903$		0			0
$904$	2.18620	+	2.79068i	0.0727119	+	0.0928166i
$905$	13.9682	+	24.1936i	0.464317	+	0.804221i
$906$		0			0
$907$	18.6114	+	10.7453i	0.617981	+	0.356791i	0.776082	−	0.630632i	$-0.217204\pi$
$907$	18.6114	+	10.7453i	0.617981	+	0.356791i	−0.158102	+	0.987423i	$0.550537\pi$
$908$	4.80383	−	10.4844i	0.159421	−	0.347936i
$909$		0			0
$910$	23.6550	+	31.6961i	0.784154	+	1.05072i
$911$	44.5039	+	25.6943i	1.47448	+	0.851291i	0.999587	−	0.0287535i	$-0.00915379\pi$
$911$	44.5039	+	25.6943i	1.47448	+	0.851291i	0.474892	+	0.880044i	$0.342487\pi$
$912$		0			0
$913$	0.417902	−	0.241276i	0.0138306	−	0.00798507i
$914$	19.0219	−	36.8411i	0.629190	−	1.21860i
$915$		0			0
$916$	−45.6642	+	32.4318i	−1.50879	+	1.07158i
$917$	23.7674	−	1.67969i	0.784869	−	0.0554683i
$918$		0			0
$919$		−	33.2245i		−	1.09597i	−0.836487	−	0.547987i	$-0.815394\pi$
$919$		−	33.2245i		−	1.09597i	0.836487	−	0.547987i	$-0.184606\pi$
$920$	17.5844	−	43.6872i	0.579739	−	1.44032i
$921$		0			0
$922$	41.9336	+	21.6513i	1.38101	+	0.713047i
$923$	4.27138	+	7.39825i	0.140594	+	0.243516i
$924$		0			0
$925$	−4.57269	+	7.92013i	−0.150349	+	0.260412i
$926$	−12.3425	+	7.92118i	−0.405599	+	0.260306i
$927$		0			0
$928$	15.3495	−	51.6805i	0.503872	−	1.69649i
$929$	23.4631	+	13.5464i	0.769800	+	0.444444i	0.832803	−	0.553569i	$-0.186735\pi$
$929$	23.4631	+	13.5464i	0.769800	+	0.444444i	−0.0630034	+	0.998013i	$0.520068\pi$
$930$		0			0
$931$	−7.38194	−	9.41962i	−0.241933	−	0.308716i
$932$	16.8261	−	1.58558i	0.551157	−	0.0519373i
$933$		0			0
$934$	−11.0456	+	0.519281i	−0.361423	+	0.0169914i
$935$		−	29.7227i		−	0.972038i
$936$		0			0
$937$			34.2337i			1.11837i	0.829044	+	0.559183i	$0.188885\pi$
$937$			34.2337i			1.11837i	−0.829044	+	0.559183i	$0.811115\pi$
$938$	4.83119	+	40.9156i	0.157744	+	1.33594i
$939$		0			0
$940$	−2.54977	−	27.0581i	−0.0831644	−	0.882538i
$941$	47.7364	−	27.5606i	1.55616	−	0.898450i	0.558543	−	0.829476i	$-0.311361\pi$
$941$	47.7364	−	27.5606i	1.55616	−	0.898450i	0.997618	−	0.0689741i	$-0.0219726\pi$
$942$		0			0
$943$	−13.8526	+	23.9934i	−0.451102	+	0.781331i
$944$	−23.2249	−	26.9381i	−0.755905	−	0.876759i
$945$		0			0
$946$	10.7709	+	16.7828i	0.350192	+	0.545655i
$947$	−13.2348	−	7.64112i	−0.430073	−	0.248303i	0.269305	−	0.963055i	$-0.413206\pi$
$947$	−13.2348	−	7.64112i	−0.430073	−	0.248303i	−0.699378	+	0.714752i	$0.746540\pi$
$948$		0			0
$949$	5.95596	+	10.3160i	0.193339	+	0.334872i
$950$	4.96946	−	9.62471i	0.161231	−	0.312267i
$951$		0			0
$952$	16.3179	+	5.26507i	0.528867	+	0.170642i
$953$	−7.58109			−0.245576			−0.122788	−	0.992433i	$-0.539183\pi$
$953$	−7.58109			−0.245576			−0.122788	+	0.992433i	$0.539183\pi$
$954$		0			0
$955$	36.2388			1.17266
$956$	35.0158	−	24.8691i	1.13249	−	0.804324i
$957$		0			0
$958$	3.61588	−	7.00313i	0.116824	−	0.226261i
$959$	3.30947	+	4.89865i	0.106868	+	0.158186i
$960$		0			0
$961$	−5.27092	+	9.12949i	−0.170030	+	0.294500i
$962$	−8.34086	+	5.35302i	−0.268920	+	0.172588i
$963$		0			0
$964$	−46.9334	−	21.5044i	−1.51162	−	0.692609i
$965$	−57.0282	−	32.9253i	−1.83580	−	1.05990i
$966$		0			0
$967$	−4.06638	+	2.34772i	−0.130766	+	0.0754977i	−0.563956	−	0.825805i	$-0.690721\pi$
$967$	−4.06638	+	2.34772i	−0.130766	+	0.0754977i	0.433190	+	0.901303i	$0.357388\pi$
$968$	11.7750	+	15.0307i	0.378461	+	0.483105i
$969$		0			0
$970$	27.8078	−	1.30732i	0.892855	−	0.0419754i
$971$	44.5685			1.43027			0.715135	−	0.698986i	$-0.246365\pi$
$971$	44.5685			1.43027			0.715135	+	0.698986i	$0.246365\pi$
$972$		0			0
$973$	26.9096	−	1.90176i	0.862681	−	0.0609675i
$974$	1.50668	+	32.0485i	0.0482772	+	1.02690i
$975$		0			0
$976$	−15.5857	−	5.43771i	−0.498885	−	0.174057i
$977$	4.78233	+	8.28324i	0.153000	+	0.265004i	0.932329	−	0.361611i	$-0.117773\pi$
$977$	4.78233	+	8.28324i	0.153000	+	0.265004i	−0.779329	+	0.626615i	$0.784440\pi$
$978$		0			0
$979$	−7.62439	+	13.2058i	−0.243677	+	0.422060i
$980$	41.3237	+	12.2655i	1.32004	+	0.391808i
$981$		0			0
$982$	7.40507	−	4.75245i	0.236305	−	0.151657i
$983$	26.0757	−	45.1644i	0.831685	−	1.44052i	−0.0650157	−	0.997884i	$-0.520710\pi$
$983$	26.0757	−	45.1644i	0.831685	−	1.44052i	0.896701	−	0.442637i	$-0.145957\pi$
$984$		0			0
$985$	−28.7592	+	16.6041i	−0.916344	+	0.529052i
$986$	27.4399	+	14.1678i	0.873863	+	0.451196i
$987$		0			0
$988$	9.57040	−	6.79712i	0.304475	−	0.216245i
$989$	−18.0988			−0.575508
$990$		0			0
$991$			41.3545i			1.31367i	0.754034	+	0.656835i	$0.228105\pi$
$991$			41.3545i			1.31367i	−0.754034	+	0.656835i	$0.771895\pi$
$992$	25.0782	+	26.4655i	0.796232	+	0.840281i
$993$		0			0
$994$	8.55364	+	3.67774i	0.271305	+	0.116651i
$995$	−12.3979	+	7.15794i	−0.393040	+	0.226922i
$996$		0			0
$997$	−45.7292	−	26.4017i	−1.44826	−	0.836152i	−0.449879	−	0.893089i	$-0.648533\pi$
$997$	−45.7292	−	26.4017i	−1.44826	−	0.836152i	−0.998378	+	0.0569376i	$0.981866\pi$
$998$	48.6799	−	31.2419i	1.54094	−	0.988946i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bi.c.559.39		80
3.2	odd	2		252.2.bi.c.223.1	yes	80
4.3	odd	2	inner	756.2.bi.c.559.13		80
7.6	odd	2	inner	756.2.bi.c.559.40		80
9.4	even	3	inner	756.2.bi.c.307.14		80
9.5	odd	6		252.2.bi.c.139.27	yes	80
12.11	even	2		252.2.bi.c.223.28	yes	80
21.20	even	2		252.2.bi.c.223.2	yes	80
28.27	even	2	inner	756.2.bi.c.559.14		80
36.23	even	6		252.2.bi.c.139.2	yes	80
36.31	odd	6	inner	756.2.bi.c.307.40		80
63.13	odd	6	inner	756.2.bi.c.307.13		80
63.41	even	6		252.2.bi.c.139.28	yes	80
84.83	odd	2		252.2.bi.c.223.27	yes	80
252.139	even	6	inner	756.2.bi.c.307.39		80
252.167	odd	6		252.2.bi.c.139.1	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.bi.c.139.1	✓	80	252.167	odd	6
252.2.bi.c.139.2	yes	80	36.23	even	6
252.2.bi.c.139.27	yes	80	9.5	odd	6
252.2.bi.c.139.28	yes	80	63.41	even	6
252.2.bi.c.223.1	yes	80	3.2	odd	2
252.2.bi.c.223.2	yes	80	21.20	even	2
252.2.bi.c.223.27	yes	80	84.83	odd	2
252.2.bi.c.223.28	yes	80	12.11	even	2
756.2.bi.c.307.13		80	63.13	odd	6	inner
756.2.bi.c.307.14		80	9.4	even	3	inner
756.2.bi.c.307.39		80	252.139	even	6	inner
756.2.bi.c.307.40		80	36.31	odd	6	inner
756.2.bi.c.559.13		80	4.3	odd	2	inner
756.2.bi.c.559.14		80	28.27	even	2	inner
756.2.bi.c.559.39		80	1.1	even	1	trivial
756.2.bi.c.559.40		80	7.6	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bi (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.41265 - 0.0664123i) q^{2} +(1.99118 - 0.187635i) q^{4} +(-2.66647 + 1.53948i) q^{5} +(1.15806 - 2.37885i) q^{7} +(2.80038 - 0.397302i) q^{8} +O(q^{10})\)	\(q+(1.41265 - 0.0664123i) q^{2} +(1.99118 - 0.187635i) q^{4} +(-2.66647 + 1.53948i) q^{5} +(1.15806 - 2.37885i) q^{7} +(2.80038 - 0.397302i) q^{8} +(-3.66455 + 2.35184i) q^{10} +(3.64870 + 2.10658i) q^{11} +(2.97309 - 1.71651i) q^{13} +(1.47795 - 3.43739i) q^{14} +(3.92959 - 0.747231i) q^{16} +2.29127i q^{17} +1.70965 q^{19} +(-5.02055 + 3.56571i) q^{20} +(5.29425 + 2.73354i) q^{22} +(-4.68317 + 2.70383i) q^{23} +(2.24003 - 3.87984i) q^{25} +(4.08594 - 2.62229i) q^{26} +(1.85954 - 4.95400i) q^{28} +(4.76517 - 8.25352i) q^{29} +(3.22265 + 5.58179i) q^{31} +(5.50152 - 1.31655i) q^{32} +(0.152169 + 3.23677i) q^{34} +(0.574276 + 8.12592i) q^{35} -2.04135 q^{37} +(2.41514 - 0.113542i) q^{38} +(-6.85549 + 5.37054i) q^{40} +(4.43693 - 2.56166i) q^{41} +(2.89849 + 1.67344i) q^{43} +(7.66048 + 3.50995i) q^{44} +(-6.43612 + 4.13059i) q^{46} +(-2.20674 + 3.82219i) q^{47} +(-4.31781 - 5.50968i) q^{49} +(2.90671 - 5.62963i) q^{50} +(5.59787 - 3.97574i) q^{52} -10.5744 q^{53} -12.9722 q^{55} +(2.29788 - 7.12178i) q^{56} +(6.18340 - 11.9758i) q^{58} +(-4.44595 - 7.70061i) q^{59} +(-3.57388 - 2.06338i) q^{61} +(4.92318 + 7.67111i) q^{62} +(7.68430 - 2.22520i) q^{64} +(-5.28509 + 9.15404i) q^{65} +(-9.53591 + 5.50556i) q^{67} +(0.429923 + 4.56233i) q^{68} +(1.35091 + 11.4410i) q^{70} +2.48841i q^{71} +3.46980i q^{73} +(-2.88373 + 0.135571i) q^{74} +(3.40422 - 0.320791i) q^{76} +(9.23662 - 6.24015i) q^{77} +(-8.87914 - 5.12638i) q^{79} +(-9.32776 + 8.04200i) q^{80} +(6.09771 - 3.91340i) q^{82} +(0.0572673 - 0.0991899i) q^{83} +(-3.52738 - 6.10959i) q^{85} +(4.20570 + 2.17150i) q^{86} +(11.0547 + 4.44959i) q^{88} +3.61933i q^{89} +(-0.640313 - 9.06033i) q^{91} +(-8.81769 + 6.26253i) q^{92} +(-2.86352 + 5.54598i) q^{94} +(-4.55872 + 2.63198i) q^{95} +(-5.53677 - 3.19666i) q^{97} +(-6.46548 - 7.49651i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 6 q^{2} - 2 q^{4} + 24 q^{8}+O(q^{10}) \) 80 * q + 6 * q^2 - 2 * q^4 + 24 * q^8	\( 80 q + 6 q^{2} - 2 q^{4} + 24 q^{8} - 10 q^{14} - 18 q^{16} - 14 q^{22} + 32 q^{25} + 28 q^{28} - 8 q^{29} + 16 q^{32} - 16 q^{37} + 84 q^{44} + 24 q^{46} - 24 q^{49} + 12 q^{50} + 48 q^{53} - 32 q^{56} - 14 q^{58} - 8 q^{64} + 40 q^{65} - 22 q^{70} - 64 q^{74} + 12 q^{77} + 40 q^{85} + 52 q^{86} + 6 q^{88} - 30 q^{92} - 20 q^{98}+O(q^{100}) \) 80 * q + 6 * q^2 - 2 * q^4 + 24 * q^8 - 10 * q^14 - 18 * q^16 - 14 * q^22 + 32 * q^25 + 28 * q^28 - 8 * q^29 + 16 * q^32 - 16 * q^37 + 84 * q^44 + 24 * q^46 - 24 * q^49 + 12 * q^50 + 48 * q^53 - 32 * q^56 - 14 * q^58 - 8 * q^64 + 40 * q^65 - 22 * q^70 - 64 * q^74 + 12 * q^77 + 40 * q^85 + 52 * q^86 + 6 * q^88 - 30 * q^92 - 20 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more